Problem: Simplify the following expression: $r = \dfrac{-4p^2 - 48p - 80}{p + 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ r =\dfrac{-4(p^2 + 12p + 20)}{p + 2} $ Then we factor the remaining polynomial: $p^2 + {12}p + {20} $ ${2} + {10} = {12}$ ${2} \times {10} = {20}$ $ (p + {2}) (p + {10}) $ This gives us a factored expression: $\dfrac{-4(p + {2}) (p + {10})}{p + 2}$ We can divide the numerator and denominator by $(p - 2)$ on condition that $p \neq -2$ Therefore $r = -4(p + 10); p \neq -2$